The piano, one of the most important instruments of western tradition, contains a certain degree of inharmonicity among the frequencies generated by each string. Many pitched acoustic instruments are designed to have partials that are close to being whole-number ratios with very low inharmonicity therefore, in music theory, and in instrument design, it is convenient, although not strictly accurate, to speak of the partials in those instruments' sounds as 'harmonics', even though they may have some degree of inharmonicity. Inharmonicity is a measure of the deviation of a partial from the closest ideal harmonic, typically measured in cents for each partial. Īn inharmonic partial is any partial that does not match an ideal harmonic. A harmonic partial is any real partial component of a complex tone that matches (or nearly matches) an ideal harmonic. The fundamental is a harmonic because it is one times itself. (See also, Fourier analysis.)Ī partial is any of the sine waves (or 'simple tones', as Ellis calls them when translating Helmholtz) of which a complex tone is composed, not necessarily with an integer multiple of the lowest harmonic.Ī harmonic is any member of the harmonic series, an ideal set of frequencies that are positive integer multiples of a common fundamental frequency. Terminology Partial, harmonic, fundamental, inharmonicity, and overtone Ī 'complex tone' (the sound of a note with a timbre particular to the instrument playing the note) 'can be described as a combination of many simple periodic waves (i.e., sine waves) or partials, each with its own frequency of vibration, amplitude, and phase'. The musical timbre of a steady tone from such an instrument is strongly affected by the relative strength of each harmonic. The musical pitch of a note is usually perceived as the lowest partial present (the fundamental frequency), which may be the one created by vibration over the full length of the string or air column, or a higher harmonic chosen by the player. Because of the typical spacing of the resonances, these frequencies are mostly limited to integer multiples, or harmonics, of the lowest frequency, and such multiples form the harmonic series. Interaction with the surrounding air causes audible sound waves, which travel away from the instrument. At the frequencies of each vibrating mode, waves travel in both directions along the string or air column, reinforcing and canceling each other to form standing waves. Pitched musical instruments are often based on an acoustic resonator such as a string or a column of air, which oscillates at numerous modes simultaneously. Sequence of frequencies Harmonics of a string showing the periods of the pure-tone harmonics (period = 1/frequency)Ī harmonic series (also overtone series) is the sequence of harmonics, musical tones, or pure tones whose frequency is an integer multiple of a fundamental frequency.

Harmonic sequence